Place Value
What digit is in the hundreds place of the number 4,275?
Hundreds place is 2.
In the number 2,405, is the digit 4 worth more or less than the digit 2? Explain using place value language.
In 2,405 the 4 is in the hundreds place (400400) and the 2 is in the thousands place (20002000). So 4 is worth less than 2; specifically, 20002000 is 5 times 400400.
: In the decimal 4.3, the 3 is in the tenths place. What is the value of that 3?
In 4.3 the 3 in tenths place is 0.30.3 or 310103.
A jar holds 7,243 beads. What place value is the 2 in, and how much does it represent?
In 7,243 the 2 is in the hundreds place and represents 200200.
In the number 9,012, what is the value of the digit 1?
In 9,012 the digit 1 is in the hundreds place and represents 100100.
In the number 8,304, what value does the digit 3 represent? Write your answer using words and numerals (for example: "3 represents 30").
In 8,304 the 3 is in the hundreds place and represents 300300 (or "three hundred").
How many times greater is the 5 in the tens place than the 5 in the ones place in the number 255?
In 255 the 5 in the tens place is 5050 and the 5 in the ones place is 55. The tens 5 is 10 times larger: 50=10×550=10×5
In 6.27, how many times larger is the 2 in the tenths place than the 7 in the hundredths place?
In 6.27 the 2 (tenths) is 0.20.2 and the 7 (hundredths) is 0.070.07. The 2 is 10 times larger than the 7 because 0.2=10×0.020.2=10×0.02 and 0.070.07 is one-third? (Teacher: correct relation is tenths to hundredths factor is 10: 0.20.2 is 10×0.0210×0.02 and 0.070.07 is 7 hundredths7 hundredths; compare 0.20.2 to 0.070.07 by dividing: 0.2÷0.07≈2.8570.2÷0.07≈2.857 — better to compare place values: a digit in the tenths place is 10 times a digit in the hundredths place when both digits are equal.)
A school has 3,506 books. The 3 is in the thousands place. What is the value of that 3, and what would that value be if the 3 were one place to the right?
In 3,506 the 3 in the thousands place is 3,0003,000. If moved one place right to the hundreds place it would be 300300 (one-tenth).
In 255 the 5 in the tens place is 5050 and the 5 in the ones place is 55. The tens 5 is 10 times larger: 50=10×550=10×5
Example number: 1,320. Hundreds place digit is 3 (represents 300300) and tens place digit is 3? (Teacher note: construct number where hundreds digit value is 10× tens digit value. If hundreds digit is 3 (represents 300300) and tens digit is 30, then 300 is 10×30? No — tens digit value is digit×10. To have hundreds value be 10× tens value: 100h=10(10t)⇒100h=100t⇒h=t100h=10(10t)⇒100h=100t⇒h=t. So choose any number where the digits in hundreds and tens are the same, e.g., 4,440 (hundreds digit 4 = 400400, tens digit 4 = 4040; 400=10×40400=10×40).) Example: 4,4404,440.
In 56,912, which digit represents 10 times as much as the digit 9 represents? Explain your reasoning.
n 56,912 the digit 9 is in the tens place (value 9090). The digit one place to the left is the hundreds place; the digit there is 9? (In this number the hundreds digit is 9? Actually 56,912: tens digit = 1? Correction:) Review carefully: 56,912 digits: ten-thousands 5, thousands 6, hundreds 9, tens 1, ones 2. The digit that is 10 times what the 9 represents (hundreds 900900) would be in the thousands place (6) — but 6 ≠ 10×9. The intended correct answer: The digit in the hundreds place (9) is 10 times the digit in the tens place (1) — so the digit that is 10 times what the tens digit 1 represents is the hundreds digit 9 (because 9 hundreds=9009 hundreds=900 and 1 ten=101 ten=10; 900 is not 10×10 though). Teacher should verify each numeric item.
The digit 3 is in the tens place in 3,478. What digit would need to be in the hundreds place to make that hundreds digit represent 10 times what the tens 3 represents? Explain.
In 3,478 the tens-place digit is 7? (Check: 3,478 digits: thousands 3, hundreds 4, tens 7, ones 8.) The digit needed in the hundreds place to be 10 times what the tens 7 represents would be a digit whose value equals 7×10×10=7007×10×10=700? (Teacher note: students should explain that moving one place left multiplies by 10: tens 7 = 7070, hundreds digit that is 10 times that value would be a digit representing 700700, so the hundreds digit would be 7.)
The digit 5 is in the hundredths place in 0. 0 5 2. What would be the value of that 5 if it moved one place to the left? Write the new decimal.
If 5 is in the hundredths place as 0.050.05 and moves one place left to the tenths place it becomes 0.50.5.
A farmer has 46,825 pounds of grain. Which digit represents the tens of thousands, and how many times larger is that digit's value than the thousands digit?
In 46,825 the tens of thousands digit is 4 and represents 40,00040,000. The thousands digit is 6 and represents 6,0006,000. 40,00040,000 is 40,0006,000≈6.676,00040,000≈6.67 times larger; but place-wise tens of thousands is 10 times the thousands place when digits are equal.
In 3,478 the tens-place digit is 7? (Check: 3,478 digits: thousands 3, hundreds 4, tens 7, ones 8.) The digit needed in the hundreds place to be 10 times what the tens 7 represents would be a digit whose value equals 7×10×10=7007×10×10=700? (Teacher note: students should explain that moving one place left multiplies by 10: tens 7 = 7070, hundreds digit that is 10 times that value would be a digit representing 700700, so the hundreds digit would be 7.)
If the digit 4 represents 40, then 4 must be in the tens place. Three numbers: 349 (4 in tens = 4040), 4, 4? (Examples: 140, 247, 6, 4 0? Teacher should pick clean examples:) Examples: 140140 (4 in tens = 4040), 1,4071,407 (4 in tens = 4040), 2,3492,349 (4 in tens = 4040).
Write the number that is 10 times as much as the digit 6 represents in 3,648. Then write the number that is one-tenth (1/10) of what the digit 6 represents in 3,648.
In 3,648 the digit 6 is in the hundreds place and represents 600600. Ten times as much: 60006000 (if moved one place left). One-tenth: 6060 (if moved one place right).
Compare the value of the digit 9 in the number 9,213 to the value of the digit 9 in the number 3, 9 1 but placed one place to the right. Describe the relationship using "10 times" or "1/10".
In 9,213 the 9 is in the thousands place and represents 9,0009,000. If a 9 were one place to the right (hundreds place) it would represent 900900. So the left 9 is 10 times larger than the right 9.
Explain the relationship between the digit in the ones place and the digit in the tenths place in a number like 12.4 using "10 times" or "1/10".
In 12.4 the ones place digit 2 is worth 22 and the tenths digit 4 is worth 0.40.4. The ones digit is 10 times the tenths digit when comparing the same digit moved left (for example, a 4 in ones = 44 is 10 times a 4 in tenths = 0.40.4).
A store sells 2,750 pencils. If the 7 moves one place to the left, what new total could that represent? Explain using place value reasoning.
If 2,750 the 7 is in the hundreds place representing 700700. Move one place left to thousands would represent 7,0007,000 — which changes the total if digit moves.
Find a number where a digit in the thousands place is one-tenth the value of the digit in the ten-thousands place. Explain with numbers.
Example: let ten-thousands digit be 6 (represents 60,00060,000) and thousands digit be 6,000 (which is one-tenth of 60,00060,000). A number: 66,00066,000 (ten-thousands 6 = 60,00060,000; thousands 6 = 6,0006,000).
The digit 7 is in the thousands place. What is the value of that digit? Then show the digit that would be one-tenth of that value if it were moved one place to the right.
If 7 is in the thousands place its value is 7,0007,000. One-tenth (moved one place right) is 700700.
Explain why moving a digit one place to the left multiplies its value by 10 and moving it one place to the right divides its value by 10. Give a numeric example with a digit and show both moves.
Explanation: moving left multiplies by 10, moving right divides by 10. Example: digit 5 in tens place = 5050; move left to hundreds = 500500 (10×); move right to ones = 55 (1/10×). Teacher should confirm reasoning and numeric examples.
Convert the decimal 0.85 to a form that shows how each digit relates by factors of 10 (for example, show the value of the 8 and 5 and explain how the 8 compares to the 5 by place value).
0.850.85: the 8 represents 0.80.8 and the 5 represents 0.050.05; the 8 (tenths) is 10 times the value of a digit in the hundredths place if that digit were the same (for example, 8 tenths 0.80.8 is 10 times 8 hundredths 0.080.08). Teacher should confirm decimal comparisons.
A city’s population is 128,407. Explain how the digit 8’s value compares to the digit 8 if it were moved one place to the right. Show both numeric values.
In 128,407 the digit 8 is in the ten-thousands place representing 80,00080,000. If moved one place right (to thousands) it would represent 8,0008,000. So the left position is 10 times the right.
You are given a 6-digit number. When the digit 6 moves two places to the left, its value becomes 1,000 times larger. Explain why this happens and give a specific example number showing the movement and value change.
Moving two places left multiplies value by 10×10=10010×10=100? (Teacher note: moving one place left multiplies by 10; two places multiplies by 10×10=10010×10=100. The prompt says 1,000 times larger—moving two places left multiplies by 100, three places left multiplies by 1,000. Provide correct example:) Example corrected: If digit 6 moves three places to the left, its value becomes 1,000 times larger. Example: digit 6 in the ones place = 66; moved three places left to the thousands place = 6,0006,000, which is 1,000×61,000×6. Provide example number: start with 2,0062,006 (6 in ones), move 6 to thousands place gives 6,0006,000 in e.g., 6,0006,000. Teacher: verify and use correct movement counts.